http://issuu.com/jeffreyheartwell/docs/edbe_8p29_-_teaching_portfolio.docx?e=22469119/31897926
Heres my teaching Portfolio
Thursday, 10 December 2015
Tuesday, 1 December 2015
Blog - #12 Final Reflection
Final Reflection:
After taking this course, I have a plethora of mathematical resources regarding the many different strands within the Mathematic Curriculum.
I have lesson plans regarding:
After taking this course, I have a plethora of mathematical resources regarding the many different strands within the Mathematic Curriculum.
I have lesson plans regarding:
- Number Sense and Numeration
- Patterning and Algebra
- Measurement
- Data Management and Probability
- Geometry and Spatial Sense
When reflecting on my teaching process regarding mathematics, I have learned that you need to differentiate your lesson plan in order to meet the needs of all of the students. I have made several connections related to teaching math, doing cross-curricular lessons in order to meet the schema of all the different students.
My thinking in J/I mathematics had made me more aware of my own teaching process, and I need to become more reflective on my teaching processes. I had to realize that there is more than one way to teach mathematics, and that my previous way of teaching does not work for all the different learners. Every student learns differently, and I need to become aware of the different instructional strategies used to differentiate each learning style.
As a reflective math teacher, I will continue to be aware of the different learning styles , and make my teaching a more interactive process. One of the resources I will need to be constantly reviewing and reflecting on is Growing success. https://www.edu.gov.on.ca/eng/policyfunding/growSuccess.pdf, this document is key for ensuring the most success for my students.
As an effective math teacher, I will need to make my teaching environment suitable for the most success, ensuring a positive learning environment. I will do this by having different cultural awareness posters around my classroom. By modelling cultural inclusiveness within my classroom, I will help the students become an active part in the learning process, leading to improving their abilities as a student, setting their own individual goals and future achievements.
Monday, 30 November 2015
Weekly Report & Reflection #11:
This week we learned about bringing technology within the classroom. The first presenter was Amberley, presenting Number Sense and Numeration, more specifically proper and improper fractions. She did a great demonstration on the board, explaining mix numbers and explaining the different processes it takes to simplify the mixed number. I already had a strong previous knowledge regarding this topic. The group activity was ordering fractions from lowest to highest, with a list of proper, improper, and mixed numbers. What I noticed, was that I did a very different process than the majority of the class, making all the numbers mixed numbers, instead of changing the numbers too improper fractions.
The second presenter was Julian, presenting Geometry 2-D shapes, explaining what a polygon is:a plan figure bounded by straight line segments to form a closed chain. He handed out a bunch of pencil crayons, and were instructed to draw various shapes on graph paper. His presentation started with having students come up to the board and guess the various shapes he drew on the board. It has been a while for myself to go over my geometrical shapes, and I got a lot of them wrong. Julian then moved onto different styles of lines, parallel lines, intersecting lines and perpendicular lines.
The next presenter was Madison, on Proportional reasoning, Ratios + equivalent ratios, and integrating technology within the classroom. We were then asked to complete a game called ratio stadium , a game where you had to eat all of the equivalent ratios in order to move forward with the game. This was a fun game to get the class engaged, while learning the topic of equivalent fractions.
Kelsey Potts presented next, on the topic patterning. She did a great job on explaining the different types of patterning using shapes and letter sequences.
The last presenter was Victoria, who presented geometry using technology. She used the Kahoot, or an application that makes learning certain topics a game. She divided the class up into table groups, and the groups competed for royalty over the class. This was a great way to promote fair play, and was the most engaging way to promote classroom participation.
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| Heartwell, 2015 |
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| Heartwell, 2015 |
Kelsey Potts presented next, on the topic patterning. She did a great job on explaining the different types of patterning using shapes and letter sequences.
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| Heartwell, 2015 |
Thanks for listening
Monday, 23 November 2015
Weekly Report & Reflection #10:
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| Heartwell, 2015 |
This week, our class discussed Data Management and Probability. Data management can be described as collecting and describing data, in ways that it can be displayed and analyzed in order to make sense out of the data.
The first presenter this week was myself, presenting the real-life applications of data management. My opening exercise, was having the students think-pair-share with their group members about where data management is used within the "real-world". I received answers from my peers ranging from average rainfall to average yearly income. I had the definitions displayed up on the board, with
mean, median, mode already defined on the white board. This way, I could adequately explain what an average was, verbally explaining it for the auditory learners, and visually representing it on the white board. My group explanation was to make the tables a shoe factory, and have them find out what the most important average was for this problem. Most of the groups came up with mode, or the most frequently occurring shoe size, as optimizing the production of shoes. This activity was designed for students connecting to the problem and reasoning to real-world problems.
The next presenter was Asma, who explained data management while using bar graphs. She had the class represent their favourite numbers up on the board. She represented this by having two people draw their results on the white boards. She facilitated this first by asking the class to get into pairs, and record the amount of times they rolled certain numbers with 10 rolls. After she had us find out what the most frequent number we rolled was. She mentioned the importance of labelling the x and y axis, as a prerequisite for comparing two unlike things.
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| Heartwell, 2015 |
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| Heartwell, 2015 |
Thanks for listening.
Saturday, 14 November 2015
Weekly Report & Reflection # 9:
Week 9: November 13th
This week in class, we went over measurement, estimation, geometry and spatial sense, and perimeter/ area. I understood all of the concepts with perimeter and area however, I was stumped
when I had to think on the spot, about what the area/ perimeter was for that shape. Today's class had 4 different presenters, presenting their knowledge on geometry and spatial sense. all of the presenters did a great job of using manipulatives, and visuals in order to teach the lesson more effectively. In today's lesson we used mirrors, isometric paper, shapes, toothpicks, marshmallows and measuring tape in order to supplement the learning process. I feel that all of these learning materials are effective for all grade levels, from grades 4 to 7. The first presenter we had was Marissa, explaining
mirror, and was actually forced to use one in this example. Transparent mirrors or (Mira) can be very helpful for explaining flips and tranformations to a student who has difficulty visually representing a flipped shape. Students can actually see the flipped picture when they look through the plastic, so it is easier for the students to trace the image onto the paper.
This week in class, we went over measurement, estimation, geometry and spatial sense, and perimeter/ area. I understood all of the concepts with perimeter and area however, I was stumped
when I had to think on the spot, about what the area/ perimeter was for that shape. Today's class had 4 different presenters, presenting their knowledge on geometry and spatial sense. all of the presenters did a great job of using manipulatives, and visuals in order to teach the lesson more effectively. In today's lesson we used mirrors, isometric paper, shapes, toothpicks, marshmallows and measuring tape in order to supplement the learning process. I feel that all of these learning materials are effective for all grade levels, from grades 4 to 7. The first presenter we had was Marissa, explaining
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| Heartwell, 2015 |
reflections, and spatial sense. She did a really effective job on showing the class how to do a reflection, using manipulatives, and the white board. This example was a great way of catering to the visual learners.
The textbook has a specific section on using Euclidean transformations (pg. 393), for explaining how to transform an object using spatial sense. This example can be represented as showing a flip of reflection, using a Mira, or a transparent mirror to reflect the shape. In the textbook they use the transparent mirror to represent flipping a shape across a side, across a line of symmetry, changing orientation, distance from the flip line, and an angle at the flip line. To the left, is a picture that I took in class, which represents how to flip a shape across a side. I found this task rather difficult without the
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| Heartwell, 2015 |
mirror, and was actually forced to use one in this example. Transparent mirrors or (Mira) can be very helpful for explaining flips and tranformations to a student who has difficulty visually representing a flipped shape. Students can actually see the flipped picture when they look through the plastic, so it is easier for the students to trace the image onto the paper.
The next presenter was Nicole, who explained 2-D and 3-D shapes to the class rather effectively. She originally had the class explain how a piece of paper is represented by a 2-D shape and a text book is represented as a 3-D shape. The activity represented below, reveals the manipulatives she used to explain vertexes, vertices, and edges on a shape. In the example below, the vertexes were represented by marshmallows, having
Nicole explain that the plural term for vertexes were vertices. I feel that this terminology will be difficult for the students to understand, and needs to be explained before the lesson takes place. On page 348 of the Small textbook, it explains the many components of 3-D shapes. It does a great job of visually representing what bases (face), vertexes/ vertices, and edges are.
The next presentation was Anthony's presentation on measurement, explaining the differences between defining perimeter and area. He explained perimeter, as being the measurement of the outside edges, and area as the amount of space within the object. His example on the board was excellent for explaining how to calculate area (LXW) and perimeter (L+L+L). The competition he had the class do was complete a series of questions on area and perimeter, and whomever completed it
the quickest got to display their work on the board. This example was a very effective way of getting the class competitive, and testing their knowledge at the same time.
In the text book (pg.448), it does a good job of visually representing area as being cubes within the shape, and hence why area is a cubed number. This example also is a good way of representing that shapes can have the same are, yet have different perimeters. What I learned from this example was how to measure perimeter the quickest and most efficient way, by recognizing similar lengths and just doubling them.
Our last presenter was Tim, on measurement, using standardized numbers. A few students within the class were asked to mark their own height on the white board, having the class estimate their height, before we actually measured it. In the text book (Small, 418), there is a great example of comparing lengths, exactly what Tim had us do in his example. He had us estimate our own height as a comparison for measuring the smallest to tallest volunteer. What I liked the most about this presentation was the real life connections, he used in order to effectively explain his topic of measurement.
All of these presentations were very well done, and gave me the resources to use in my upcoming placement. Each presenter was very knowledgeable about their topic, which would give the students a more effective understanding of the topic. Thanks for the treats Joyce!!
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| Heartwell, 2015 |
The next presentation was Anthony's presentation on measurement, explaining the differences between defining perimeter and area. He explained perimeter, as being the measurement of the outside edges, and area as the amount of space within the object. His example on the board was excellent for explaining how to calculate area (LXW) and perimeter (L+L+L). The competition he had the class do was complete a series of questions on area and perimeter, and whomever completed it
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| Heartwell, 2015 |
In the text book (pg.448), it does a good job of visually representing area as being cubes within the shape, and hence why area is a cubed number. This example also is a good way of representing that shapes can have the same are, yet have different perimeters. What I learned from this example was how to measure perimeter the quickest and most efficient way, by recognizing similar lengths and just doubling them.
Our last presenter was Tim, on measurement, using standardized numbers. A few students within the class were asked to mark their own height on the white board, having the class estimate their height, before we actually measured it. In the text book (Small, 418), there is a great example of comparing lengths, exactly what Tim had us do in his example. He had us estimate our own height as a comparison for measuring the smallest to tallest volunteer. What I liked the most about this presentation was the real life connections, he used in order to effectively explain his topic of measurement.
All of these presentations were very well done, and gave me the resources to use in my upcoming placement. Each presenter was very knowledgeable about their topic, which would give the students a more effective understanding of the topic. Thanks for the treats Joyce!!
Monday, 2 November 2015
Weekly Report & Reflection #7:
Weekly Report:
Unfortunately during this week I was absent, due to a stomach flu.
Reflection:
The chapter reading was on Patterning and Algebra. This chapter was mainly about patterns representing different regularities, always revealing an element of repetition. The main idea I got was patterns representing the same item over and over again, being represented in many different ways. Some ways of representing data in different ways can be represented by algebra, explaining the relationships by analyzing the change. I also learned that variables are an efficient way of representing relationships between quantities.
What I found interesting was the many different ways a pattern can be represented; through shapes, numbers, sizes, letters, colours, literally anything can be represented by a pattern. The part that I did not understand was the section on diagonal patterns. This section within in the textbook,
(Small, Marion, pg 612), in particular I did not understand. After reading the context of the problem, I then understand the pattern, and could continue it. The big idea with this section was using appropriate manipulative's in order to represent a pattern. Being able to represent a pattern with both the manipulative's and numbers is the gold standard when trying to explain patterns to students. Some interesting manipulative's I learned about within this chapter include; counters, attribute blocks, pattern blocks, geometric shapes, linking cubes, and toothpicks. The most effective manipulative I found was the toothpicks, because I can foresee myself using this example within my upcoming placement, as a tool to explain growth patterns and counting the sides on shapes.
This example in particular is extremely effective because I can show the pattern of number of sides, having the students physically being able to deconstruct the shapes and recognize how many sides there are. The students can group these manipulative's specifically and show the growth pattern as well. I feel like relationships and functions will be one of the hardest parts to explain to the students, being able to extract my previous knowledge and present it in a way the students can understand and construct their own ideas and strategies from.
An effective website I found while researching how to teach algebra was; this video. It goes over the many different steps needed to understand algebra efficiently. I especially liked this video because it went over a lot of different learning strategies, simplifying each step.
Unfortunately during this week I was absent, due to a stomach flu.
Reflection:
The chapter reading was on Patterning and Algebra. This chapter was mainly about patterns representing different regularities, always revealing an element of repetition. The main idea I got was patterns representing the same item over and over again, being represented in many different ways. Some ways of representing data in different ways can be represented by algebra, explaining the relationships by analyzing the change. I also learned that variables are an efficient way of representing relationships between quantities.
What I found interesting was the many different ways a pattern can be represented; through shapes, numbers, sizes, letters, colours, literally anything can be represented by a pattern. The part that I did not understand was the section on diagonal patterns. This section within in the textbook,
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| (Heartwell, 2015) |
This example in particular is extremely effective because I can show the pattern of number of sides, having the students physically being able to deconstruct the shapes and recognize how many sides there are. The students can group these manipulative's specifically and show the growth pattern as well. I feel like relationships and functions will be one of the hardest parts to explain to the students, being able to extract my previous knowledge and present it in a way the students can understand and construct their own ideas and strategies from.
An effective website I found while researching how to teach algebra was; this video. It goes over the many different steps needed to understand algebra efficiently. I especially liked this video because it went over a lot of different learning strategies, simplifying each step.
Monday, 26 October 2015
Weekly Report & Reflection #6:
Weekly Reflection:
This weeks class was focused on the big ideas such as; rate, ratio, and proportions. The main themes of this week were the big ideas for ratios, and proportional thinking. I understood a lot of the lecture, but had trouble understanding the ratios being expanded from a reduced form to a expanded form, and visually representing this. Matt did an excellent job of explaining ratios this week with visually representing the ratios while drawing a picture. I had a problem converting 7/8 to 14/16 and
drawing the border, trying to enlarge the original photo. Matt's first example of ratios was how many eyes a person has, having two eyes to one body being represented as 2:1.
This example is an extremely effective tool when using this for elementary school students, getting an overall grasp of what ratios are. The picture to the left represents the problem that Matt gave us as a class to figure out. This problem was answered in many ways by the class, with some students free handing the drawing, to some drawing a border around what they needed to draw, and transferring the image.
I did a mixture of both, originally free handing it, and then drawing a border to see where I went wrong. In the end I was only a couple boxes off the original image. Matt then had the class think about proportional thinking, more specifically how two ratios can equal the same thing, when expanded. A specific example Matt gave us was when he said represent 1/3 in 7th's which was 7/21.
Things that I learned this Lesson:
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| Heartwell, 2015 |
This example is an extremely effective tool when using this for elementary school students, getting an overall grasp of what ratios are. The picture to the left represents the problem that Matt gave us as a class to figure out. This problem was answered in many ways by the class, with some students free handing the drawing, to some drawing a border around what they needed to draw, and transferring the image.
I did a mixture of both, originally free handing it, and then drawing a border to see where I went wrong. In the end I was only a couple boxes off the original image. Matt then had the class think about proportional thinking, more specifically how two ratios can equal the same thing, when expanded. A specific example Matt gave us was when he said represent 1/3 in 7th's which was 7/21.
Things that I learned this Lesson:
- How to expand ratios
- Proportional ratios
- Equivalent ratios
Points I would Like to Make:
- Visually representing the image while drawing a picture on a grid was a very effective teaching strategy
- Group discussions about the final product and how the students got there was extremely effective
Weekly Report:
What I learned this week within the text was proportional reasoning, ratios, number lines, and solving ratio problems. The area that I related to the most to within this chapter was the common errors and misconceptions area. More specifically relating percent to multiplication inappropriately. I had trouble recognizing 4= _ % of 8 when in reality for is 1/2 or 0.5 of 8. The method that was suggested to use to fix this problem was recognizing that 4 was 1/2 of 8. This was a lot easier to visually represent this problem on paper, than mentally representing this.
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